what is causing my armature to warp the model so badly when rotating it's arm, how can i fix this?
Yes, your weight painting is off, you'll have to use envelopes (not the best solution) or manually adjust the weights, so that the upper arm does not effect the chest anymore.
Select the armature, then the guy. 
CRTL + TAB -> choose weight paint.
Use the brush tools to adjust your weights.